数学与蒙太古语法

Mathematics and Montague Grammar

从数学的角度建立语法的组织系统可以取得描写上的系统性、严密性和一致性。蒙太古语法主要是关于语义学的理论,因此在严格意义上,应把蒙太古语法称作蒙太古语义学。任何一种语义学都必须说明:什么是意义;句子意义的运算;语义学与句法学之间的关系。本文将从以下几个方面探索如何可用数学的基本原理取得上述的目的。

This paper attempts to give a methematical characterization of Montague Grammar. It consistsof five parts: (1) The definition of the meaning of the sentence in terms of function; (2) The characteristic function and the semantic value of the sentence; (3) Functional application and the Fregean Principle; (4) The composite of two functions and the indirect calculation of the semantic value of the sentence; (5) Homomorphism from syntactic algebra to semantic algebra.